Core Geometry in the Real World

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Part 1: Rectangles in Real Life

Show your working and include the correct units in every answer.

1. A rectangular garden is 6 m long and 4 m wide. Calculate its perimeter.

2. Calculate the area of the same garden.

3. Which calculation is most useful for each task? Choose perimeter or area.

a) Finding the length of edging needed around the garden: ____________________

b) Finding the space available for planting: ____________________

c) Finding the amount of fencing needed around a garden: ____________________

d) Finding the amount of exercise space inside a dog area: ____________________

4. A rectangular dog area is 8 m long and 5 m wide. Calculate its area and perimeter.

Part 2: Accuracy and Reasoning

5. A student says, “The area of the 6 m by 4 m garden is 10 m² because 6 + 4 = 10.” Check the solution. Explain the error and give the correct answer.

6. A measurement is out by 1 cm. Explain why even a small error can matter when planning edging, fencing or planting space.

7. Sketch a rectangle to represent the dog area. Label the length and width, write the perimeter and area formulas, and show your working.

8. A gardener has 20 m of edging and wants to surround the 6 m by 4 m garden. Is there enough edging? Complete a reasonableness check and explain your answer.

Answer Key and Marking Guidance

1. Perimeter = 6 + 4 + 6 + 4 = 20 m. Award 1 mark for the correct method and 1 mark for the answer with units.

2. Area = 6 × 4 = 24 m². Award 1 mark for multiplying length by width and 1 mark for the correct units.

3. a) Perimeter; b) Area; c) Perimeter; d) Area. Award 1 mark for each correct choice.

4. Area = 8 × 5 = 40 m². Perimeter = 8 + 5 + 8 + 5 = 26 m. Award 1 mark for each correct calculation and 1 mark for suitable units.

5. The student has added the two dimensions instead of multiplying them. The correct area is 6 × 4 = 24 m². Award up to 2 marks for identifying the error and correcting the solution.

6. A 1 cm error can change the amount of material needed or the available space. It may cause edging or fencing not to fit accurately, or lead to an incorrect planting or exercise area. Award up to 2 marks for a clear real-world explanation.

7. The sketch should be a labelled rectangle with 8 m and 5 m shown, using the correct perimeter and area formulas and working. Award up to 3 marks for the sketch and labels, formulas, and working.

8. The garden needs 20 m of edging because its perimeter is 20 m. Therefore, yes, there is exactly enough. A reasonableness check could note that two 6 m sides and two 4 m sides give about 20 m altogether. Award up to 2 marks for the comparison and explanation.

Partner explanation: Students should be able to describe which measurement they calculated, why it was useful, and how they checked that the answer was reasonable.